Discrete transformations in the Thomson Problem

A significantly lower upper limit to minimum energy solutions of the electrostatic Thomson Problem is reported. A point charge is introduced to the origin of each N-charge solution. This raises the total energy by N as an upper limit to each (N + 1)-charge solution. Minimization of energy to U(N + 1) is well fit with for up to N = 500. The energy distribution due to this displacement exhibits correspondences with shell-filling behavior in atomic systems. This work may aid development of more efficient and innovative numerical search algorithms to obtain N-charge configurations having global energy minima and yield new insights to atomic structure.